An ab initio study of linear dihydrogen-bonded complexes containing LiH (acting as a proton acceptor) was undertaken. The complexes studied were LiH.HF, LiH.HCN, and LiH.HCCH. Equilibrium geometries and harmonic vibrational frequencies were computed at various levels of theory using a 6-31++G(d,p) basis set. It was found that the LiH.HF complex was not stable at all levels of theory. The relative stabilities of H-bonded and D-bonded isotopomers of LiH.HCN and LiH.HCCH were determined by differences in zero-point vibrational frequencies. For LiH.HCN isotopomers, it was found that the LiD.HCN was favored over LiH.DCN with a relative stability of 54 cm(-1) calculated at the Quadratic Configuration Interaction-Singles and Doubles level. Similarly, LiD.HCCH is favored over LiH.DCCH, with a lower value for the relative stability. The relative stabilities of the H-bonded and D-bonded species LiH.HCCD and LiH.DCCH indicated that the D-bonded complex was energetically favored, in accordance with the Buckingham-Liu theory.